We propose an adaptive bandwidth selector via cross validation for local M-estimators in locally stationary processes. We prove asymptotic optimality of the procedure under mild conditions on the underlying parameter curves. The results are applicable to a wide range of locally stationary processes such linear and nonlinear processes. A simulation study shows that the method works fairly well also in misspecified situations.
"Cross validation for locally stationary processes." Ann. Statist. 47 (4) 2145 - 2173, August 2019. https://doi.org/10.1214/18-AOS1743